%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP358-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HYXgJgkpyV true
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:18 PM UTC 2025
% Result : Unsatisfiable 0.53s 0.95s
% Output : Refutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : GRP358-1 : TPTP v9.2.0. Released v2.5.0.
% 0.07/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HYXgJgkpyV true
% 0.13/0.37 % Computer : n018.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Oct 1 14:26:53 EDT 2025
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Running portfolio for 300 s
% 0.13/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Number of cores: 8
% 0.13/0.37 % Python version: Python 3.6.8
% 0.13/0.37 % Running in FO mode
% 0.50/0.61 % Total configuration time : 435
% 0.50/0.61 % Estimated wc time : 1092
% 0.50/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.53/0.95 % Solved by fo/fo7.sh.
% 0.53/0.95 % done 291 iterations in 0.192s
% 0.53/0.95 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.53/0.95 % SZS output start Refutation
% 0.53/0.95 thf(sk_c2_type, type, sk_c2: $i).
% 0.53/0.95 thf(sk_c8_type, type, sk_c8: $i).
% 0.53/0.95 thf(sk_c5_type, type, sk_c5: $i).
% 0.53/0.95 thf(sk_c4_type, type, sk_c4: $i).
% 0.53/0.95 thf(identity_type, type, identity: $i).
% 0.53/0.95 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.53/0.95 thf(sk_c6_type, type, sk_c6: $i).
% 0.53/0.95 thf(inverse_type, type, inverse: $i > $i).
% 0.53/0.95 thf(sk_c3_type, type, sk_c3: $i).
% 0.53/0.95 thf(sk_c1_type, type, sk_c1: $i).
% 0.53/0.95 thf(sk_c7_type, type, sk_c7: $i).
% 0.53/0.95 thf(prove_this_31, conjecture,
% 0.53/0.95 (~( ( ( multiply @ X5 @ sk_c8 ) != ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ X5 ) != ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ X4 @ sk_c8 ) != ( X3 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) != ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) ) ))).
% 0.53/0.95 thf(zf_stmt_0, negated_conjecture,
% 0.53/0.95 (( ( multiply @ X5 @ sk_c8 ) != ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ X5 ) != ( sk_c6 ) ) | ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ X4 @ sk_c8 ) != ( X3 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ X3 ) != ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) != ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c8 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 0.53/0.95 thf(zip_derived_cl33, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.53/0.95 (((multiply @ X0 @ sk_c8) != (sk_c6))
% 0.53/0.95 | ((inverse @ X0) != (sk_c6))
% 0.53/0.95 | ((inverse @ X1) != (sk_c7))
% 0.53/0.95 | ((multiply @ X1 @ sk_c7) != (sk_c6))
% 0.53/0.95 | ((inverse @ X2) != (sk_c8))
% 0.53/0.95 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 0.53/0.95 | ((inverse @ X3) != (sk_c8))
% 0.53/0.95 | ((multiply @ X3 @ sk_c8) != (X4))
% 0.53/0.95 | ((multiply @ sk_c8 @ X4) != (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c8) != (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.53/0.95 thf(zip_derived_cl34, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.53/0.95 (((multiply @ X0 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c6))
% 0.53/0.95 | ((inverse @ X0) != (sk_c6))
% 0.53/0.95 | ((inverse @ X1) != (sk_c7))
% 0.53/0.95 | ((multiply @ X1 @ sk_c7) != (sk_c6))
% 0.53/0.95 | ((inverse @ X2) != (multiply @ sk_c7 @ sk_c6))
% 0.53/0.95 | ((multiply @ X2 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c7))
% 0.53/0.95 | ((inverse @ X3) != (multiply @ sk_c7 @ sk_c6))
% 0.53/0.95 | ((multiply @ X3 @ (multiply @ sk_c7 @ sk_c6)) != (X4))
% 0.53/0.95 | ((multiply @ (multiply @ sk_c7 @ sk_c6) @ X4) != (sk_c7))
% 0.53/0.95 | ((inverse @ (multiply @ sk_c7 @ sk_c6)) != (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8)))),
% 0.53/0.95 inference('local_rewriting', [status(thm)], [zip_derived_cl33])).
% 0.53/0.95 thf(associativity, axiom,
% 0.53/0.95 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.53/0.95 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl47, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.53/0.95 (((multiply @ X0 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c6))
% 0.53/0.95 | ((inverse @ X0) != (sk_c6))
% 0.53/0.95 | ((inverse @ X1) != (sk_c7))
% 0.53/0.95 | ((multiply @ X1 @ sk_c7) != (sk_c6))
% 0.53/0.95 | ((inverse @ X2) != (multiply @ sk_c7 @ sk_c6))
% 0.53/0.95 | ((multiply @ X2 @ (multiply @ sk_c7 @ sk_c6)) != (sk_c7))
% 0.53/0.95 | ((inverse @ X3) != (multiply @ sk_c7 @ sk_c6))
% 0.53/0.95 | ((multiply @ X3 @ (multiply @ sk_c7 @ sk_c6)) != (X4))
% 0.53/0.95 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ X4)) != (sk_c7))
% 0.53/0.95 | ((inverse @ (multiply @ sk_c7 @ sk_c6)) != (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) != (sk_c8)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl2])).
% 0.53/0.95 thf(prove_this_26, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 0.53/0.95 thf(zf_stmt_1, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 0.53/0.95 thf(zip_derived_cl28, plain,
% 0.53/0.95 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.53/0.95 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl41, plain,
% 0.53/0.95 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl51, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((multiply @ identity @ X0)
% 0.53/0.95 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.53/0.95 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl100, plain,
% 0.53/0.95 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl74])).
% 0.53/0.95 thf(prove_this_20, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 0.53/0.95 thf(zf_stmt_2, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 0.53/0.95 thf(zip_derived_cl22, plain,
% 0.53/0.95 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.53/0.95 thf(zip_derived_cl275, plain,
% 0.53/0.95 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.53/0.95 = (sk_c2))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl22])).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl288, plain,
% 0.53/0.95 ((((identity) = (sk_c2))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl275, zip_derived_cl2, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl289, plain,
% 0.53/0.95 ((((inverse @ sk_c3) = (sk_c8)) | ((identity) = (sk_c2)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl288])).
% 0.53/0.95 thf(prove_this_14, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 0.53/0.95 thf(zf_stmt_3, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 0.53/0.95 thf(zip_derived_cl16, plain,
% 0.53/0.95 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.53/0.95 thf(zip_derived_cl295, plain,
% 0.53/0.95 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8))
% 0.53/0.95 | ((inverse @ sk_c3) = (sk_c8)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl289, zip_derived_cl16])).
% 0.53/0.95 thf(zip_derived_cl303, plain,
% 0.53/0.95 ((((inverse @ sk_c3) = (sk_c8))
% 0.53/0.95 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl295])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl89, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl74])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl86, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl74])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl565, plain,
% 0.53/0.95 ((((inverse @ sk_c3) = (sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl303, zip_derived_cl532])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl89, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl74])).
% 0.53/0.95 thf(zip_derived_cl574, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl89])).
% 0.53/0.95 thf(zip_derived_cl604, plain,
% 0.53/0.95 ((((sk_c3) = (inverse @ sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl565, zip_derived_cl574])).
% 0.53/0.95 thf(prove_this_25, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 0.53/0.95 thf(zf_stmt_4, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 0.53/0.95 thf(zip_derived_cl27, plain,
% 0.53/0.95 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.53/0.95 thf(zip_derived_cl574, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl89])).
% 0.53/0.95 thf(zip_derived_cl594, plain,
% 0.53/0.95 ((((sk_c1) = (inverse @ sk_c8)) | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl574])).
% 0.53/0.95 thf(prove_this_19, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 0.53/0.95 thf(zf_stmt_5, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 0.53/0.95 thf(zip_derived_cl21, plain,
% 0.53/0.95 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.53/0.95 thf(zip_derived_cl976, plain,
% 0.53/0.95 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c2))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl594, zip_derived_cl21])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl992, plain,
% 0.53/0.95 ((((identity) = (sk_c2))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl976, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl993, plain,
% 0.53/0.95 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c2)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl992])).
% 0.53/0.95 thf(prove_this_13, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 0.53/0.95 thf(zf_stmt_6, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 0.53/0.95 thf(zip_derived_cl15, plain,
% 0.53/0.95 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.53/0.95 thf(zip_derived_cl1011, plain,
% 0.53/0.95 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl993, zip_derived_cl15])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1023, plain,
% 0.53/0.95 ((((sk_c8) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1011, zip_derived_cl532])).
% 0.53/0.95 thf(zip_derived_cl1024, plain,
% 0.53/0.95 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1023])).
% 0.53/0.95 thf(zip_derived_cl1276, plain,
% 0.53/0.95 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((sk_c8) = (sk_c7))
% 0.53/0.95 | ((sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl604, zip_derived_cl1024])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl1279, plain,
% 0.53/0.95 ((((identity) = (sk_c7)) | ((sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1276, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1280, plain,
% 0.53/0.95 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1279])).
% 0.53/0.95 thf(prove_this_8, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.53/0.95 thf(zf_stmt_7, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 0.53/0.95 thf(zip_derived_cl10, plain,
% 0.53/0.95 ((((inverse @ sk_c3) = (sk_c8)) | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl38, plain,
% 0.53/0.95 ((((multiply @ sk_c8 @ sk_c3) = (identity))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl96, plain,
% 0.53/0.95 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl74])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl560, plain,
% 0.53/0.95 ((((sk_c3) = (inverse @ sk_c8)) | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl96, zip_derived_cl532])).
% 0.53/0.95 thf(prove_this_7, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.53/0.95 thf(zf_stmt_8, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 0.53/0.95 thf(zip_derived_cl9, plain,
% 0.53/0.95 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.53/0.95 thf(zip_derived_cl744, plain,
% 0.53/0.95 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl560, zip_derived_cl9])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl750, plain,
% 0.53/0.95 ((((identity) = (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl744, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl751, plain,
% 0.53/0.95 ((((inverse @ sk_c8) = (sk_c6)) | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl750])).
% 0.53/0.95 thf(zip_derived_cl1312, plain,
% 0.53/0.95 ((((inverse @ sk_c7) = (sk_c6))
% 0.53/0.95 | ((identity) = (sk_c7))
% 0.53/0.95 | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1280, zip_derived_cl751])).
% 0.53/0.95 thf(zip_derived_cl1324, plain,
% 0.53/0.95 ((((identity) = (sk_c7)) | ((inverse @ sk_c7) = (sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1312])).
% 0.53/0.95 thf(prove_this_4, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 0.53/0.95 thf(zf_stmt_9, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 0.53/0.95 thf(zip_derived_cl6, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl36, plain,
% 0.53/0.95 ((((multiply @ sk_c7 @ sk_c4) = (identity))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl91, plain,
% 0.53/0.95 ((((sk_c4) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl74])).
% 0.53/0.95 thf(prove_this_3, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) ) ))).
% 0.53/0.95 thf(zf_stmt_10, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c8 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 0.53/0.95 thf(zip_derived_cl5, plain,
% 0.53/0.95 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.53/0.95 thf(zip_derived_cl184, plain,
% 0.53/0.95 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.53/0.95 = (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl5])).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl190, plain,
% 0.53/0.95 ((((identity) = (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8))
% 0.53/0.95 | ((multiply @ sk_c7 @ sk_c6) = (sk_c8)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl184, zip_derived_cl2, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl191, plain,
% 0.53/0.95 ((((multiply @ sk_c7 @ sk_c6) = (sk_c8)) | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl190])).
% 0.53/0.95 thf(prove_this_10, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.53/0.95 thf(zf_stmt_11, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 0.53/0.95 thf(zip_derived_cl12, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7)) | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl39, plain,
% 0.53/0.95 ((((multiply @ sk_c7 @ sk_c4) = (identity))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl92, plain,
% 0.53/0.95 ((((sk_c4) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl74])).
% 0.53/0.95 thf(prove_this_9, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.53/0.95 thf(zf_stmt_12, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 0.53/0.95 thf(zip_derived_cl11, plain,
% 0.53/0.95 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_12])).
% 0.53/0.95 thf(zip_derived_cl138, plain,
% 0.53/0.95 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.53/0.95 = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl11])).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl143, plain,
% 0.53/0.95 ((((identity) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl138, zip_derived_cl2, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl144, plain,
% 0.53/0.95 ((((inverse @ sk_c8) = (sk_c6)) | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl143])).
% 0.53/0.95 thf(zip_derived_cl215, plain,
% 0.53/0.95 ((((inverse @ (multiply @ sk_c7 @ sk_c6)) = (sk_c6))
% 0.53/0.95 | ((identity) = (sk_c6))
% 0.53/0.95 | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl191, zip_derived_cl144])).
% 0.53/0.95 thf(zip_derived_cl217, plain,
% 0.53/0.95 ((((identity) = (sk_c6))
% 0.53/0.95 | ((inverse @ (multiply @ sk_c7 @ sk_c6)) = (sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl215])).
% 0.53/0.95 thf(zip_derived_cl1331, plain,
% 0.53/0.95 ((((inverse @ (multiply @ sk_c7 @ (inverse @ sk_c7))) = (sk_c6))
% 0.53/0.95 | ((identity) = (sk_c7))
% 0.53/0.95 | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1324, zip_derived_cl217])).
% 0.53/0.95 thf(zip_derived_cl574, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl89])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl580, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl574, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl88, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl74])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl126, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl88, zip_derived_cl74])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1340, plain,
% 0.53/0.95 ((((identity) = (sk_c6))
% 0.53/0.95 | ((identity) = (sk_c7))
% 0.53/0.95 | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl1331, zip_derived_cl580, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1341, plain,
% 0.53/0.95 ((((identity) = (sk_c7)) | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1340])).
% 0.53/0.95 thf(zip_derived_cl1280, plain,
% 0.53/0.95 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1279])).
% 0.53/0.95 thf(zip_derived_cl751, plain,
% 0.53/0.95 ((((inverse @ sk_c8) = (sk_c6)) | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl750])).
% 0.53/0.95 thf(zip_derived_cl574, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl89])).
% 0.53/0.95 thf(zip_derived_cl848, plain,
% 0.53/0.95 ((((sk_c8) = (inverse @ sk_c6)) | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl751, zip_derived_cl574])).
% 0.53/0.95 thf(zip_derived_cl1314, plain,
% 0.53/0.95 ((((sk_c7) = (inverse @ sk_c6))
% 0.53/0.95 | ((identity) = (sk_c7))
% 0.53/0.95 | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1280, zip_derived_cl848])).
% 0.53/0.95 thf(zip_derived_cl1326, plain,
% 0.53/0.95 ((((identity) = (sk_c7)) | ((sk_c7) = (inverse @ sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1314])).
% 0.53/0.95 thf(zip_derived_cl1377, plain,
% 0.53/0.95 ((((sk_c7) = (inverse @ identity))
% 0.53/0.95 | ((identity) = (sk_c7))
% 0.53/0.95 | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1341, zip_derived_cl1326])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1379, plain,
% 0.53/0.95 ((((sk_c7) = (identity))
% 0.53/0.95 | ((identity) = (sk_c7))
% 0.53/0.95 | ((identity) = (sk_c7)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1377, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1410, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.53/0.95 (((multiply @ X0 @ sk_c6) != (sk_c6))
% 0.53/0.95 | ((inverse @ X0) != (sk_c6))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (sk_c6))
% 0.53/0.95 | ((inverse @ X2) != (sk_c6))
% 0.53/0.95 | ((multiply @ X2 @ sk_c6) != (identity))
% 0.53/0.95 | ((inverse @ X3) != (sk_c6))
% 0.53/0.95 | ((multiply @ X3 @ sk_c6) != (X4))
% 0.53/0.95 | ((multiply @ sk_c6 @ X4) != (identity))
% 0.53/0.95 | ((inverse @ sk_c6) != (sk_c6))
% 0.53/0.95 | ((sk_c6) != (sk_c8)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl47, zip_derived_cl1380, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1380, zip_derived_cl1380, zip_derived_cl532,
% 0.53/0.95 zip_derived_cl1380, zip_derived_cl0, zip_derived_cl1380,
% 0.53/0.95 zip_derived_cl0, zip_derived_cl1380, zip_derived_cl1380,
% 0.53/0.95 zip_derived_cl0, zip_derived_cl1380, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1380, zip_derived_cl0, zip_derived_cl1380,
% 0.53/0.95 zip_derived_cl1380, zip_derived_cl0, zip_derived_cl1380,
% 0.53/0.95 zip_derived_cl0])).
% 0.53/0.95 thf(prove_this_27, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 0.53/0.95 thf(zf_stmt_13, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 0.53/0.95 thf(zip_derived_cl29, plain,
% 0.53/0.95 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c8)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_13])).
% 0.53/0.95 thf(zip_derived_cl89, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl74])).
% 0.53/0.95 thf(zip_derived_cl424, plain,
% 0.53/0.95 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.53/0.95 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl89])).
% 0.53/0.95 thf(prove_this_21, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 0.53/0.95 thf(zf_stmt_14, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 0.53/0.95 thf(zip_derived_cl23, plain,
% 0.53/0.95 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_14])).
% 0.53/0.95 thf(zip_derived_cl462, plain,
% 0.53/0.95 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.53/0.95 = (sk_c2))
% 0.53/0.95 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl424, zip_derived_cl23])).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl478, plain,
% 0.53/0.95 ((((identity) = (sk_c2))
% 0.53/0.95 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl462, zip_derived_cl2, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl479, plain,
% 0.53/0.95 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c2)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl478])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1421, plain,
% 0.53/0.95 ((((sk_c4) = (sk_c6)) | ((identity) = (sk_c2)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl479, zip_derived_cl1380, zip_derived_cl532])).
% 0.53/0.95 thf(prove_this_15, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 0.53/0.95 thf(zf_stmt_15, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 0.53/0.95 thf(zip_derived_cl17, plain,
% 0.53/0.95 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 0.53/0.95 | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_15])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl1394, plain,
% 0.53/0.95 ((((sk_c4) = (sk_c6)) | ((multiply @ sk_c8 @ sk_c2) = (identity)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl17, zip_derived_cl1380, zip_derived_cl532,
% 0.53/0.95 zip_derived_cl1380])).
% 0.53/0.95 thf(zip_derived_cl1619, plain,
% 0.53/0.95 ((((multiply @ sk_c8 @ identity) = (identity))
% 0.53/0.95 | ((sk_c4) = (sk_c6))
% 0.53/0.95 | ((sk_c4) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1421, zip_derived_cl1394])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1629, plain,
% 0.53/0.95 ((((sk_c8) = (identity)) | ((sk_c4) = (sk_c6)) | ((sk_c4) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1619, zip_derived_cl532])).
% 0.53/0.95 thf(zip_derived_cl1630, plain,
% 0.53/0.95 ((((sk_c4) = (sk_c6)) | ((sk_c8) = (identity)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1629])).
% 0.53/0.95 thf(prove_this_28, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 0.53/0.95 thf(zf_stmt_16, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 0.53/0.95 thf(zip_derived_cl30, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_16])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl42, plain,
% 0.53/0.95 ((((multiply @ sk_c8 @ sk_c1) = (identity))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl101, plain,
% 0.53/0.95 ((((sk_c1) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl74])).
% 0.53/0.95 thf(prove_this_22, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) ) ))).
% 0.53/0.95 thf(zf_stmt_17, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c2 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 0.53/0.95 thf(zip_derived_cl24, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_17])).
% 0.53/0.95 thf(zip_derived_cl156, plain,
% 0.53/0.95 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.53/0.95 = (sk_c2))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl101, zip_derived_cl24])).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl169, plain,
% 0.53/0.95 ((((identity) = (sk_c2))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl156, zip_derived_cl2, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl170, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7)) | ((identity) = (sk_c2)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl169])).
% 0.53/0.95 thf(prove_this_16, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) ) ))).
% 0.53/0.95 thf(zf_stmt_18, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 0.53/0.95 ( ( multiply @ sk_c8 @ sk_c2 ) = ( sk_c7 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 0.53/0.95 thf(zip_derived_cl18, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c8 @ sk_c2) = (sk_c7)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_18])).
% 0.53/0.95 thf(zip_derived_cl177, plain,
% 0.53/0.95 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7))
% 0.53/0.95 | ((inverse @ sk_c4) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl170, zip_derived_cl18])).
% 0.53/0.95 thf(zip_derived_cl181, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7))
% 0.53/0.95 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl177])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl564, plain,
% 0.53/0.95 ((((inverse @ sk_c4) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl181, zip_derived_cl532])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl600, plain,
% 0.53/0.95 ((((multiply @ sk_c7 @ sk_c4) = (identity)) | ((sk_c8) = (sk_c7)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl564, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1380, plain, (((sk_c7) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1379])).
% 0.53/0.95 thf(zip_derived_cl1433, plain,
% 0.53/0.95 ((((sk_c4) = (identity)) | ((sk_c8) = (identity)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl600, zip_derived_cl1380, zip_derived_cl0,
% 0.53/0.95 zip_derived_cl1380])).
% 0.53/0.95 thf(zip_derived_cl1637, plain,
% 0.53/0.95 ((((sk_c6) = (identity))
% 0.53/0.95 | ((sk_c8) = (identity))
% 0.53/0.95 | ((sk_c8) = (identity)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1630, zip_derived_cl1433])).
% 0.53/0.95 thf(zip_derived_cl1639, plain,
% 0.53/0.95 ((((sk_c8) = (identity)) | ((sk_c6) = (identity)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1637])).
% 0.53/0.95 thf(zip_derived_cl144, plain,
% 0.53/0.95 ((((inverse @ sk_c8) = (sk_c6)) | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl143])).
% 0.53/0.95 thf(zip_derived_cl1647, plain,
% 0.53/0.95 ((((inverse @ identity) = (sk_c6))
% 0.53/0.95 | ((sk_c6) = (identity))
% 0.53/0.95 | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1639, zip_derived_cl144])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1657, plain,
% 0.53/0.95 ((((identity) = (sk_c6))
% 0.53/0.95 | ((sk_c6) = (identity))
% 0.53/0.95 | ((identity) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1647, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl532, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl86])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1694, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X2) != (identity))
% 0.53/0.95 | ((inverse @ X3) != (identity))
% 0.53/0.95 | ((X3) != (X4))
% 0.53/0.95 | ((X4) != (identity))
% 0.53/0.95 | ((identity) != (identity))
% 0.53/0.95 | ((identity) != (sk_c8)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl1410, zip_derived_cl1658, zip_derived_cl532,
% 0.53/0.95 zip_derived_cl1658, zip_derived_cl1658, zip_derived_cl1658,
% 0.53/0.95 zip_derived_cl1658, zip_derived_cl1658, zip_derived_cl532,
% 0.53/0.95 zip_derived_cl1658, zip_derived_cl1658, zip_derived_cl532,
% 0.53/0.95 zip_derived_cl1658, zip_derived_cl0, zip_derived_cl1658,
% 0.53/0.95 zip_derived_cl519, zip_derived_cl1658, zip_derived_cl1658])).
% 0.53/0.95 thf(zip_derived_cl1695, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.53/0.95 (((identity) != (sk_c8))
% 0.53/0.95 | ((X4) != (identity))
% 0.53/0.95 | ((X3) != (X4))
% 0.53/0.95 | ((inverse @ X3) != (identity))
% 0.53/0.95 | ((X2) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((X0) != (identity)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1694])).
% 0.53/0.95 thf(zip_derived_cl1706, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X2) != (identity))
% 0.53/0.95 | ((inverse @ X3) != (identity))
% 0.53/0.95 | ((X3) != (identity))
% 0.53/0.95 | ((identity) != (sk_c8)))),
% 0.53/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1695])).
% 0.53/0.95 thf(prove_this_11, conjecture,
% 0.53/0.95 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.53/0.95 thf(zf_stmt_19, negated_conjecture,
% 0.53/0.95 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 0.53/0.95 thf(zip_derived_cl13, plain,
% 0.53/0.95 ((((inverse @ sk_c5) = (sk_c6)) | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_19])).
% 0.53/0.95 thf(zip_derived_cl1, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_inverse])).
% 0.53/0.95 thf(zip_derived_cl40, plain,
% 0.53/0.95 ((((multiply @ sk_c6 @ sk_c5) = (identity))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl74, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl94, plain,
% 0.53/0.95 ((((sk_c5) = (multiply @ (inverse @ sk_c6) @ identity))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl74])).
% 0.53/0.95 thf(prove_this_12, conjecture,
% 0.53/0.95 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) ) ))).
% 0.53/0.95 thf(zf_stmt_20, negated_conjecture,
% 0.53/0.95 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 0.53/0.95 ( ( inverse @ sk_c8 ) = ( sk_c6 ) )),
% 0.53/0.95 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 0.53/0.95 thf(zip_derived_cl14, plain,
% 0.53/0.95 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('cnf', [status(esa)], [zf_stmt_20])).
% 0.53/0.95 thf(zip_derived_cl231, plain,
% 0.53/0.95 ((((multiply @ (multiply @ (inverse @ sk_c6) @ identity) @ sk_c8)
% 0.53/0.95 = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl14])).
% 0.53/0.95 thf(zip_derived_cl2, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.53/0.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.53/0.95 inference('cnf', [status(esa)], [associativity])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl236, plain,
% 0.53/0.95 ((((multiply @ (inverse @ sk_c6) @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((inverse @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl231, zip_derived_cl2, zip_derived_cl0])).
% 0.53/0.95 thf(zip_derived_cl237, plain,
% 0.53/0.95 ((((inverse @ sk_c8) = (sk_c6))
% 0.53/0.95 | ((multiply @ (inverse @ sk_c6) @ sk_c8) = (sk_c6)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl236])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl0, plain,
% 0.53/0.95 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.53/0.95 inference('cnf', [status(esa)], [left_identity])).
% 0.53/0.95 thf(zip_derived_cl1658, plain, (((identity) = (sk_c6))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1657])).
% 0.53/0.95 thf(zip_derived_cl1677, plain,
% 0.53/0.95 ((((inverse @ sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl237, zip_derived_cl1658, zip_derived_cl1658,
% 0.53/0.95 zip_derived_cl519, zip_derived_cl0, zip_derived_cl1658])).
% 0.53/0.95 thf(zip_derived_cl574, plain,
% 0.53/0.95 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl532, zip_derived_cl89])).
% 0.53/0.95 thf(zip_derived_cl1780, plain,
% 0.53/0.95 ((((sk_c8) = (inverse @ identity)) | ((sk_c8) = (identity)))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl1677, zip_derived_cl574])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1783, plain,
% 0.53/0.95 ((((sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1780, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1784, plain, (((sk_c8) = (identity))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1783])).
% 0.53/0.95 thf(zip_derived_cl1800, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X2) != (identity))
% 0.53/0.95 | ((inverse @ X3) != (identity))
% 0.53/0.95 | ((X3) != (identity))
% 0.53/0.95 | ((identity) != (identity)))),
% 0.53/0.95 inference('demod', [status(thm)],
% 0.53/0.95 [zip_derived_cl1706, zip_derived_cl1784])).
% 0.53/0.95 thf(zip_derived_cl1801, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.53/0.95 (((X3) != (identity))
% 0.53/0.95 | ((inverse @ X3) != (identity))
% 0.53/0.95 | ((X2) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((X0) != (identity)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1800])).
% 0.53/0.95 thf(zip_derived_cl1808, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X2) != (identity))
% 0.53/0.95 | ((inverse @ identity) != (identity)))),
% 0.53/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1801])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1809, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X2) != (identity))
% 0.53/0.95 | ((identity) != (identity)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1808, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1810, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.53/0.95 (((X2) != (identity))
% 0.53/0.95 | ((inverse @ X2) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((X0) != (identity)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1809])).
% 0.53/0.95 thf(zip_derived_cl1811, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((inverse @ identity) != (identity)))),
% 0.53/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1810])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1812, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((X1) != (identity))
% 0.53/0.95 | ((identity) != (identity)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1811, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1813, plain,
% 0.53/0.95 (![X0 : $i, X1 : $i]:
% 0.53/0.95 (((X1) != (identity))
% 0.53/0.95 | ((inverse @ X1) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((X0) != (identity)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1812])).
% 0.53/0.95 thf(zip_derived_cl1814, plain,
% 0.53/0.95 (![X0 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((inverse @ identity) != (identity)))),
% 0.53/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1813])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1815, plain,
% 0.53/0.95 (![X0 : $i]:
% 0.53/0.95 (((X0) != (identity))
% 0.53/0.95 | ((inverse @ X0) != (identity))
% 0.53/0.95 | ((identity) != (identity)))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1814, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1816, plain,
% 0.53/0.95 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1815])).
% 0.53/0.95 thf(zip_derived_cl1817, plain, (((inverse @ identity) != (identity))),
% 0.53/0.95 inference('eq_res', [status(thm)], [zip_derived_cl1816])).
% 0.53/0.95 thf(zip_derived_cl519, plain, (((inverse @ identity) = (identity))),
% 0.53/0.95 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.53/0.95 thf(zip_derived_cl1818, plain, (((identity) != (identity))),
% 0.53/0.95 inference('demod', [status(thm)], [zip_derived_cl1817, zip_derived_cl519])).
% 0.53/0.95 thf(zip_derived_cl1819, plain, ($false),
% 0.53/0.95 inference('simplify', [status(thm)], [zip_derived_cl1818])).
% 0.53/0.95
% 0.53/0.95 % SZS output end Refutation
% 0.53/0.95
% 0.53/0.95
% 0.53/0.95 % Terminating...
% 1.62/1.04 % Runner terminated.
% 1.62/1.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------